The aim of this study is geostatistical analysis and detection of anomalous elements in the Bardaskan area (in geological map of Bardaskan on scale 1:100,000 which is provided by the GSI organization). The study area is located in Khorasan province of Iran. Due to the availability of lithogeochemical regular data in the region as well as the importance of exploration of metal minerals in order to simplify and summarize the geochemical map, geostatistical methods were used to identify the mineralization potential of the region. Initially, using single-variable and multivariate statistical methods, anomalous elements were separated. Then, the thresholds (various communities) for the titanium element that was most likely to be anomalous were identified. Using these limits, the discriminant analysis was applied to the elements. Titanium, iron and magnesium elements were identified as the main mineral elements in the region. These elements indicate mineralization in the mafic bed rocks. Finally the map of the concentration of titanium element was mapped across the region with Kriging interpolation method. As a result, two anomalies of the titanium element in the region were identified.
The statistics are a vast array of maths that study ways to collect, summarize, and conclude data. This science applies to a wide range of academic sciences from physics and social sciences to anthropology, as well as business, government, and industry. Statistics is the science and practice of human development through the use of experimental data. Statistics are based on the theory of statistics, which is a branch of applied mathematics. In statistical theory, random events and uncertainty are modeled by probability theory. In this science, studying and judging on various subjects is done on the basis of a society and judgment about a particular person is not at all questionable [
The geostatistics, which is the most important statistical theory based on the field concept of the place, is the theory of regional variables. The regional variable is defined as any environment property whose numerical values are distributed in one-, two-, or three-dimensional sampling space. The spatial variations of a regional variable have two structural and random components. One of the main goals of spatial statistics is to provide an appropriate model for describing the regional variable by taking into account the structural and random variability components. This section of spatial statistics is called geostatistics [
Identification and recognition of anomalies from background is an essential issue in geochemical exploration [
The Bardaskan area is in the geological map on scale 1:100,000 is one of the rectangular sheets of Kashmar map which is on scale 1:250,000. The study area is in geographical coordinates 57˚00' - 57˚30' eastern longitude and 35˚00' - 35˚30' northern latitude. The range of the Bardaskan sheet is among the cities of Khorasan Razavi province of Iran. Major geological subdivisions of Iran and geology map of Bardaskan area are shown in
- Magnesite.
- Fluorite.
- Bauxite.
- Chromite.
- Copper.
- Turquoise.
- Coal.
- Iron.
Considering the existence of different economic mines in Khorasan Razavi province, the Bardaskan region, which is one of the most susceptible areas in the province, was selected to investigate exploratory geochemistry by applying statistical methods.
- Geomorphology:
From the morphological viewpoint, the Bards can area can be studied in two separate parts which are distinguished from each other by the Daroone fault. The part of the area located above the fault is a mountain range with a wide variety. But the southern part of the mentioned fault, except for the southeast hills, is a continuation of the outcrops of the Uzbak mountain range, with an average elevation of 850 meters above sea level, which occurs at a vast surface of quaternary units such as alluvial terraces, alluvial fans, clay and salt formations [
- Stratigraphy:
Precambrian: This section is located south of Takanar main fault. The wedge form of this section, which is located between the Daroone and Taknar faults. Based on the existence of outcrops from the Taknar-Precambrian formation, and the covering of the Paleozoic and Mesozoic rocks it has been designated as an erosional window indicating the uplift of Precambrian Paleozoic basement rock of the Iran central tectonic zone in the Tertiary Age [
Taknar formation: The Taknar formation consists of a thick sequence of schists, tuffs, green schists, and quartzite sandstones that have undergone a mild metamorphism in the sub-greenschist facies. In this sequence there are massive metamorphic rhyolites and rhyodacites. One of the important features of this formation is its contact with two intrusive masses. One Intrusive Mass of Precambrian that includes granite and granitoid, and another mass of granite whose time of influence is Eocene-Oligocene [
The type of sampling is lithogeochemical and is performed according to a regular network. A total of 483 lithogeochemical samples were collected from the area. Samples have been analyzed using ICP-AES method. Sampling network location is shown in
Correlation is used to test relationships between quantitative variables or categorical variables. In other words, it’s a measure of how things are related. The study of how variables are correlated is called correlation analysis [
Correlations are useful because if you can find out what relationship variables have, you can make predictions about future behavior [
In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types [
• Agglomerative Method:
This is a “bottom up” approach: each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.
• Divisive Method:
This is a “top down” approach: all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy (see
Discriminant analysis is used as a tool for the separation of communities [
δ k ( x ) = − μ k Σ − 1 x + 1 2 μ k Σ − 1 μ k + log (πk)
you can see the steps in discriminant analysis method in
The following plot shows the linear classification boundaries that result when a sample data set of two variables is modelled using linear discriminant analysis (
The results of the samples analysis which were taken regularly from rock units were analyzed using single-variable statistics. Regarding the field limitations of the elements in the area as well as their measured value in the samples, Ti, Cu, Mo and Zn elements are known as anomalous elements in the region.The result of this study is presented in
Using Spearman method, correlation coefficients among the elements in the region were investigated.
Considering the need for clustering and creating enough visibility to understand mineral elements and also the separation of these elements from the elements that have created the area’s rocks, hierarchical cluster method was used (
Elements | Min | Max | Average | Std. Deviation | Variance | Skewness | Kurtosis | Median | Mode | Anomalous limit |
---|---|---|---|---|---|---|---|---|---|---|
Cr | 12 | 271 | 72 | 42 | 1788 | 2 | 5 | 59.000 | 47.0 | 100 |
Mn | 27 | 3170 | 596 | 541 | 292,995 | 1 | 1 | 420.000 | 108.0 | 950 |
Ni | 0 | 147 | 16 | 19 | 371 | 3 | 12 | 7.000 | 4.0 | 75 |
Pb | 0 | 4000 | 40 | 234 | 54,811 | 12 | 182 | 5.800 | 0.0 | 12.5 |
Ti | 156 | 19,900 | 3690 | 4027 | 16,218,242 | 2 | 3 | 2210.000 | 1020 | 5000 |
Fe | 2120 | 143,000 | 39225 | 27,387 | 750,058,457 | 1 | 1 | 30,150.000 | 24,400 | - |
Hg | 0 | 1 | 0 | 0 | 0 | 2 | 5 | 0.0000 | 0.00 | 0.08 |
Ag | 0 | 28 | 1 | 2 | 4 | 10 | 113 | 0.8600 | 0.80 | 0.07 |
Co | 0 | 331 | 12 | 24 | 576 | 9 | 101 | 5.650 | 0.8 | 25 |
Cu | 2 | 43,100 | 437 | 3000 | 9,001,803 | 10 | 122 | 15.900 | 5.6 | 55 |
Mo | 0 | 43 | 4 | 5 | 24 | 4 | 27 | 2.500 | 0.9 | 1.5 |
Sb | 0 | 20 | 2 | 2 | 3 | 5 | 34 | 1.200 | 1.2 | 0.2 |
Zn | 0 | 6200 | 119 | 374 | 140,037 | 12 | 167 | 47.800 | 138.0 | 70 |
Sn | 0 | 37 | 3 | 3 | 9 | 7 | 62 | 3.000 | 2.0 | 2 |
W | 0 | 19 | 7 | 3 | 11 | 0 | 0 | 7.100 | 6.0 | 1.5 |
Euclidean distance was used. Titanium, iron, and magnesium appear together, which reflects the mineralization in the mafic bed rock. In the correlation coefficient (
Regarding the choice of the titanium element as target element, its histogram was drawn and the type of distribution of the statistical society of that, was detected as log-normal distribution (
The separation of communities from the titanium probability chart is considered to be an important point in determining the limits of the society and thus determining the geochemical threshold. For this purpose, a line is fitted to the probability diagram, and the fracture points of the diagram are investigated.
In this section, LDA was performed using the limits obtained in the previous section.
Au | Cr | Mn | Ni | Pb | Sr | Ba | Be | Ti | Fe | Hg | Ag | As | Bi | Co | Cu | Mo | Sb | Zn | Sn | W | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Au | 1 | ||||||||||||||||||||
Cr | 0.101 | 1 | |||||||||||||||||||
Mn | 0.022 | 0.423 | 1 | ||||||||||||||||||
Ni | −0.035 | 0.637 | 0.618 | 1 | |||||||||||||||||
Pb | 0.277 | 0.117 | 0.266 | 0.123 | 1 | ||||||||||||||||
Sr | −0.097 | 0.333 | 0.230 | 0.479 | −0.153 | 1 | |||||||||||||||
Ba | 0.127 | −0.189 | 0.089 | −0.172 | 0.381 | −0.323 | 1 | ||||||||||||||
Be | 0.041 | −0.088 | 0.322 | 0.031 | 0.273 | −0.324 | 0.474 | 1 | |||||||||||||
Ti | −0.060 | 0.383 | 0.779 | 0.680 | 0.100 | 0.421 | 0.090 | 0.302 | 1 | ||||||||||||
Fe | 0.099 | 0.559 | 0.791 | 0.727 | 0.252 | 0.327 | 0.010 | 0.228 | 0.780 | 1 | |||||||||||
Hg | 0.020 | −0.105 | −0.064 | 0.069 | 0.188 | −0.062 | 0.306 | 0.075 | 0.013 | −0.030 | 1 | ||||||||||
Ag | 0.109 | −0.376 | −0.237 | −0.339 | 0.238 | −0.181 | 0.302 | 0.101 | −0.265 | −0.253 | 0.445 | 1 | |||||||||
As | 0.298 | 0.275 | 0.302 | 0.221 | 0.376 | 0.036 | 0.273 | 0.189 | 0.271 | 0.439 | 0.014 | 0.056 | 1 | ||||||||
Bi | 0.317 | 0.247 | 0.363 | 0.149 | 0.466 | −0.169 | 0.211 | 0.321 | 0.202 | 0.425 | −0.055 | 0.053 | 0.614 | 1 | |||||||
Co | 0.005 | 0.554 | 0.648 | 0.697 | 0.179 | 0.356 | 0.020 | 0.128 | 0.675 | 0.775 | −0.058 | −0.298 | 0.480 | 0.435 | 1 | ||||||
Cu | 0.200 | 0.456 | 0.543 | 0.442 | 0.461 | 0.100 | 0.164 | 0.198 | 0.445 | 0.618 | 0.108 | 0.037 | 0.485 | 0.626 | 0.523 | 1 | |||||
Mo | 0.267 | 0.044 | −0.263 | −0.294 | 0.246 | −0.304 | 0.137 | −0.014 | −0.413 | −0.222 | 0.060 | 0.265 | 0.144 | 0.277 | −0.226 | 0.122 | 1 | ||||
Sb | 0.282 | 0.403 | 0.555 | 0.401 | 0.483 | 0.093 | 0.269 | 0.279 | 0.503 | 0.631 | −0.028 | −0.090 | 0.671 | 0.605 | 0.560 | 0.606 | 0.023 | 1 | |||
Zn | 0.165 | 0.412 | 0.815 | 0.544 | 0.495 | 0.086 | 0.177 | 0.440 | 0.681 | 0.747 | −0.059 | −0.104 | 0.452 | 0.523 | 0.590 | 0.640 | −0.106 | 0.653 | 1 | ||
Sn | 0.053 | −0.375 | −0.113 | −0.341 | 0.210 | −0.428 | 0.520 | 0.457 | −0.066 | −0.162 | 0.159 | 0.255 | 0.006 | 0.078 | −0.229 | −0.050 | 0.146 | 0.073 | −0.024 | 1 | |
W | 0.182 | −0.199 | −0.316 | −0.386 | 0.232 | −0.555 | 0.381 | 0.204 | −0.386 | −0.336 | 0.263 | 0.198 | 0.060 | 0.181 | −0.309 | −0.056 | 0.241 | −0.022 | −0.202 | 0.380 | 1 |
communities are considered with consideration of all the elements and finally the accuracy of this separation is given in
Titanium | Group members predicted | Total | ||||
---|---|---|---|---|---|---|
First | Second | Third | ||||
Cross Validation | Counts | First | 81 | 14 | 0 | 95 |
Second | 56 | 259 | 12 | 327 | ||
Third | 0 | 1 | 59 | 60 | ||
% | First | 85.3 | 14.7 | 0.0 | 100.0 | |
Second | 17.1 | 79.2 | 3.7 | 100.0 | ||
Third | 0.0 | 1.7 | 98.3 | 100.0 |
separated. In
1st community: Ti.
2nd community: Be, Fe, Ba, Hg, Mn.
3rd community: Ni, Zn, W, Ag, Bi, Au, Sn, Cr, Pb, Sr, As, Mo, Cu, Co, Sb.
In
After performing various affairs and identifying the relationship between the elements and also recognizing the titanium element as important element in the region. Regarding the behavior of this element, which has been studied in different parts, in the form of anomalies, a map of the highest concentration limits in the region should be prepared. This map represents the best locations for detailed exploration and further exploration. The Kriging Interpolation method (with a variogram that was extracted from a radial survey) was used to prepare this map.
The map is shown in
・ The Bardaskan area, located in the Razavi Khorasan province of Iran, is one of the areas with metallic mineralization potential.
・ Regarding the importance of geostatistical methods, at first lithogeochemical samples with single-variable methods were investigated. Correlation between elements was calculated. Then hierarchical clustering using squared Euclidean distance method was performed.
・ Hierarchical clustering, which according to the previous results identified the elements of titanium, iron, and magnesium as the mineralization phase, also showed the rock-forming phase.
・ By carefully examining the histogram and cumulative probability diagram of the titanium, the log-normal distribution was determined for this element.
・ By separating communities from the logarithmic probability diagram, the geochemical limits were determined 1000, 3000 and 9000 ppm for the titanium element, respectively.
・ Due to the specified limits, the decision was made to carry out the Linear Discriminant Analysis (LDA). The results of this analysis were another proof of the phase of mineralization and rock-forming of the area and confirmation of the correct choice of titanium.
・ Finally, in order to provide a better visibility of the titanium element distribution in the area, a map was prepared. The Kriging interpolation method was used to prepare this map.
The authors declare no conflicts of interest regarding the publication of this paper.
Alahgholi, S., Shirazy, A. and Shirazi, A. (2018) Geostatistical Studies and Anomalous Elements Detection, Bardaskan Area, Iran. Open Journal of Geology, 8, 697-710. https://doi.org/10.4236/ojg.2018.87041